Over which interval is the graph of f (x) = - x^+3x+8 increasing?

It is increasing in the interval (-∞, 3/2).

Step-by-step explanation:

y = - x^2 + 3x + 8

The derivative is:

dy/dx = - 2x + 3

This is the slope of tangent to the curve so when f (x) is increasing

-2x + 3 > 0

-2x > - 3

x < 3/2

So it is increasing in the interval (-∞, 3/2)